A widely used technique for acquiring nuclear magnetic resonance (NMR) data both in the laboratory and in well logging, uses an RF pulse sequence known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence. As is known, after a wait time that precedes each pulse sequence, known as polarization time, a ninety degree pulse that rotates the magnetization to the x-y plane. The spins begin to precess around B0 and dephase due to inhomogeneity in the magnetic field and spin-spin interactions. After a certain time delay, a one hundred eighty degree pulse is applied to cause the spins which are dephasing in the transverse plane to refocus. Refocusing leads to an echo that is detected by the NMR instrument. By repeated application of one hundred eighty degree pulses, a series of “spin echoes” appear, and the train of echoes is measured and processed.
It is recognized that “ringing” is a problem encountered when using pulsed NMR techniques. Ringing noise can arise, for example, from electromagnetic (EM) cross-talk or magneto-acoustic vibrations in the transmitting and/or receiving antennas or circuits. Noise coherent with the pulse sequence always exist in raw NMR data and must be taken into account in order to extract accurate NMR signal parameters from the raw data. The ringing noise is in addition to random thermal noise that always exists in NMR data. Signal averaging of raw data sets can reduce the random noise but cannot reduce coherent noise. The NMR raw data in general consist of NMR signal, ringing noise, and random noise. The ringing noise usually consists of a constant or weakly time-dependent offset plus a time-dependent transient. The transient rapidly decays to zero and is significant only at early times. For CPMG and similar spin-echo generating pulse sequences the transient is produced by the 90-degree pulse and usually has the same phase as the signal. The transient typically persists for a relatively few echoes whereas the offsets are present on all echoes.
The ringing offsets are assumed to be independent of the phase of the 90-degree radio-frequency (rf) pulse that creates the transverse magnetization in CPMG and similar pulse sequences. One prior art method for removing the offset signal involves acquisition of two phase alternated CPMG spin-echo sequences using 90-degree pulses that are phase shifted with respect to one another by 180 degrees. The phase shift of the 90-degree pulse causes the reversal of the sign of the NMR signal and the transient signal. The offset remains unchanged. Therefore subtracting the two phase-alternated pairs (PAP) eliminates the offset. This method is widely used in NMR laboratory spectrometers as well as in NMR well-logging tools. One of the drawbacks of the PAPs method is that it requires combining two acquisitions. This limits the vertical resolution for well-logging measurements made in non-overlapping measurement mode to twice the antenna aperture (see e.g., McKeon et al. SPWLA Transactions, 1999). The PAP method can also fail to satisfactorily remove the offset if it changes significantly from one acquisition to the next due, for example, to changes in the conductivity of the rock formation that are not fully compensated for by the gain corrections that are separately applied to each of the CPMGs in a PAP. Another limitation of the PAP method is that it only removes the offset and does not remove or reduce the effects of the transient noise, i.e., the 90-degree ringing.
Another approach (U.S. Pat. No. 6,121,774) for removing ringing from a pulse sequence is to acquire NMR raw data that contains only the ringing signals, i.e., the NMR signal is not present. The ringing signals can be recorded and used to correct the raw data. For example, one approach proposes a method whereby “spoiling pulses” are applied at the end of each CPMG in order to cancel the NMR signal so that ringing signals can be recorded. The ringing signals are averaged to reduce random noise and then subtracted from each echo in the CPMG.
Another method (Sigal et al. in SPE Paper No. 63215) for removing the offset signal from NMR well-logging data has been proposed to estimate the offset (also referred to as the bias) signal by adding adjacent CPMG echo trains that are acquired with 90-degree pulses differing in phase by 180 degrees. The offset is then subtracted from each echo to obtain bias corrected NMR data. This method of estimating bias is most appropriate when the formation signal remains constant during the acquisition of two adjacent CPMGs. However, in practice the formation properties and therefore the formation signal changes from one acquisition to another. Furthermore the method does not effectively remove transient ringing. The prior art methods attempt to remove the ringing from the raw data prior to processing the data in order to extract the NMR signal.